The relation between stretched-exponential relaxation and the vibrational density of states in glassy disordered systems

B. Cui; R. Milkus; A. Zaccone

doi:10.1016/j.physleta.2016.12.003

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arXiv · 1701.05037

The relation between stretched-exponential relaxation and the vibrational density of states in glassy disordered systems

B. Cui·R. Milkus·A. Zaccone

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Abstract

Amorphous solids or glasses are known to exhibit stretched-exponential decay over broad time intervals in several of their macroscopic observables: intermediate scattering function, dielectric relaxation modulus, time-elastic modulus etc. This behaviour is prominent especially near the glass transition. In this Letter we show, on the example of dielectric relaxation, that stretched-exponential relaxation is intimately related to the peculiar lattice dynamics of glasses. By reformulating the Lorentz model of dielectric matter in a more general form, we express the dielectric response as a function of the vibrational density of states (DOS) for a random assembly of spherical particles interacting harmonically with their nearest-neighbours. Surprisingly we find that near the glass transition for this system (which coincides with the Maxwell rigidity transition), the dielectric relaxation is perfectly consistent with stretched-exponential behaviour with Kohlrausch exponents $0.56 < \beta < 0.65$, which is the range where exponents are measured in most experimental systems. Crucially, the root cause of stretched-exponential relaxation can be traced back to soft modes (boson-peak) in the DOS.

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B. Cui, R. Milkus, A. Zaccone. 2017-01-18. The relation between stretched-exponential relaxation and the vibrational density of states in glassy disordered systems. https://doi.org/10.1016/j.physleta.2016.12.003

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